Finite Group DatabasebetaFinite Group DatabasebetaOrder 10449.
38 conjugacy classes of subgroups.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | #16812515 | C3 | 1 | 3 | yes | maximal |
| 2 | C43×C9⋊C9 | C3 | 1 | 1 | yes | maximal, characteristic |
| 3 | #11923958 | — | 3 | 3 | no | — |
| 4 | C3×C9×C43 | — | 3 | 1 | no | — |
| 5 | C3×C9×C43 | C32 | 1 | 1 | yes | characteristic |
| 6 | C32×C43 | H(3,𝔽3) | 1 | 1 | yes | characteristic |
| 7 | C9×C43 | — | 3 | 1 | no | — |
| 8 | C9×C43 | — | 9 | 1 | no | — |
| 9 | C43⋊C9 | — | 9 | 3 | no | — |
| 10 | #6882 | — | 43 | 1 | no | maximal, Sylow |
| 11 | C3×C43 | — | 3 | 1 | no | — |
| 12 | C3×C43 | #732 | 1 | 1 | yes | characteristic |
| 13 | #733 | — | 43 | 3 | no | — |
| 14 | C9⋊C9 | C43⋊C3 | 1 | 1 | yes | characteristic |
| 15 | C43 | #6882 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 16 | 3−1+2 | — | 129 | 3 | no | — |
| 17 | C3×C9 | — | 3 | 1 | no | — |
| 18 | C3×C9 | C3×C43⋊C3 | 1 | 1 | yes | characteristic |
| 19 | C32 | C32⋊(C43⋊C3) | 1 | 1 | yes | characteristic |
| 20 | C9 | — | 3 | 1 | no | — |
| 21 | C9 | — | 9 | 1 | no | — |
| 22 | C9 | — | 387 | 3 | no | — |
| 23 | C3 | — | 3 | 1 | no | — |
| 24 | C3 | #16812513 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 15. C43 | #6882 | semidirect |